“Information is all that matters!” The author1 is a doctor of physics completed at the Warsaw University of Technology in 2004. The subject of the doctorate were the method of estimation and noise reduction in the time series. The author is also a specialist in finance (especially in derivatives such as options), mathematics, informatics, and philosophy. At the beginning of his career for several years worked as a scientist at the Max-Planck Institute in Dresden and Warsaw University of Technology. He is the author of several scientific content items. For a long time he worked as a quant in financial institutions. He is currently a chief executive officer and a minority shareholder in the company Quant Technology2. For more information, please visit www.wonabru.com. The author is the founder and creator of Informationism. 1 E-mail: [email protected] 2 www.quant-technology.com Informationism from Philosophy to Quantitative Trading (4th edition)– Krzysztof Urbanowicz 1 “Logic is the way to independence” “To all that are above the schemes” - wonabru Informationism from Philosophy to Quantitative Trading (4th edition)– Krzysztof Urbanowicz 2 Introduction 5 What is Informationism? 7 Theory of the origin of the Universe 10 Question: Why Me? 13 Information theory - the foundation of Informationism 15 Principles of information 17 The generalization of the de'Broglie waves - information carrier 20 Experiment to proof Theory of Information 21 General description of idea of the experiment 21 Setup the experiment 24 25 Results 25 Conclusions 26 Principles of conservation of matter and information 27 The main principles of Informationism 27 Difficult questions that can be answered from the standpoint of Informationism 29 What is information? 29 Is there any absolute constant in our Universe in time and space? 29 How to explain gravity on the basis of Information Theory? 29 Synchronous communication: a higher level of thinking in the twenty-first century 30 Mysticism and Information Theory 31 What is energy? 31 Why is that information is spontaneously self-created? The three bodies problem. 32 What is the problem with the Second Law of Thermodynamics? Why do religious people claim that this is evidence for the existence of God? 33 Corpuscular-wave duality 34 Intuitive evidence that the matter can be converted to information. 34 Practical application of Informationism 35 The Theory of Objective Values 35 Objective Value Theory in finance 35 Normalization in Objective Value space 37 Examples 38 Objective Value (ObV) Option pricing model for power-law distribution 40 Put option 46 Greek letter Delta 47 Informationism from Philosophy to Quantitative Trading (4th edition)– Krzysztof Urbanowicz 3 Difference to Lisa Borland approach 47 Results for option pricing. 48 Delta Hedge Strategy based on the Objective Value Option Pricing theory 53 How Objective value theory works in trend forecasting of stochastic systems? 55 Statistical forecasting 58 Generalized gaussianity evaluation 59 The Wonabru investment method 60 Results based on WONABRU methodology 61 Introducing Shannon entropy into portfolio optimization 63 Equations of portfolio optimization 65 The explanation of introducing entropy to portfolio optimization 66 Stochastic processes in financial data – how to evaluate it? 73 Entropy estimation for a time series in the noise absence 75 Influence of noise on correlation integral 76 Noise estimation for financial time series 79 How quickly and properly calculate Value-at-Risk for the whole portfolio? 80 Examples of automated strategies 83 Strategy I 83 Strategy II 83 Strategy III 83 Strategy IV 84 Strategy V 84 Strategy VI 84 Bibliography 85 Informationism from Philosophy to Quantitative Trading (4th edition)– Krzysztof Urbanowicz 4 Introduction Someone may ask: Why am I introducing philosophy or even some kind of God to story about physics and finance? So I should refer to this question. One should start from the very beginning, if she/he wanted to build success. Success is created on strong basis, fundamentals, absolute Truth, objectives, fully logical proved and could not be discredited. Everybody should have the possibility to perform one’s Logic, in the same manner, with the understanding. I’ve started from looking something stable, absolute in time and space, in the Universe. The Theory of Creation of Universe shows how one may play with logic. I was looking also for universal principles which govern the Universe. Physics gives such a possibility. The Theory of Information is making huge unification of nowadays physical Laws. This is the basis. Without this, I could not make any progress in practical creation of investment strategies, etc. Automated investment strategies appears as the practical implementation and consequence of fundamentals. I must state that, there is an absolute in our Universe. This is Action (Logic). Action for physicists. Logic is for Informationists. I am Informationist, means Informationism is understandable for me and fully logical. How the quant trading can fetch values from Informationism? Trading is very tough staff. It needs very good understanding of science (not only physics). Well performing in programming. One also should disclaim intuition, emotions and feelings in trading, because thus make you lose. Apart above leaves just logic. Everything in this World, in this Universe, is logical, so can be understood by each person. Informationism gives you the way to build your own Absolut, because without an Absolute, you won't do anything successful. Absolut gives you strength not to change your mind, if your logic says that solution should be close, but emotions want you go back. Your Absolute makes you to be convinced and this is very important when things are starting to go badly. On the other hand, absolute value means objective, means really existing. On the Objective Value Theory (ObV) are based many strategies in this book. Why objective value is so important? It is, because, objective is additive. In the next step it is stated to be commutative. One can then, perform any arithmetic on such values like divisions, multiplications etc... About objective values are referring Gödel’s Theory of Incompleteness3. When values are additive, one can build principles, like principle of conservation. Principle, that, objective values are limited. Last one principle is that, on creation of the objective value the minimal dynamic is performed (minimal action or minimal dynamic entropy principle). I will talk about the last one in details later. You will see that, starting from nothing, vacuum, emptiness one can recognize principles ruling the Universe. This rules we can use for prediction. For example: if something is minimized or going to equilibrium, we can use it to found out the trend. Informationism is very helpful, because even if we stuck in dead 3 http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems Informationism from Philosophy to Quantitative Trading (4th edition)– Krzysztof Urbanowicz 5 point, like in developing some theory, every time we can refer to our Absolute and find solution. Quant Trading, means automated trading, also every aspects of success in your life, is based on solid backgrounds. Here we have Informationism. This is my grounds and also can be yours. In the next section we will explain the main ideas of Informationism and Theory of Information and you will acknowledge, why it is so important. Informationism from Philosophy to Quantitative Trading (4th edition)– Krzysztof Urbanowicz 6 What is Informationism? Informationism is the philosophy of science, based on Information Theory. Information Theory creates a binding of matter with the information. Information Theory is the foundation of Informationism and we devote to this theory entire chapter later in this book. In short, this theory says that, the action, as because it is discrete, can be converted to information. There is well-known corpuscular-wave duality found by de’Broglie. This duality is saying, that each moving mass generates wave. We generalized this theory also to not moving masses, but for which mass is changing. Mass can be diminished, when energy is released by e.g. nuclear reaction. Strong fields binds all neutron and protons together in kernel of atom. This energy, which keeps atom kernel together, increases the mass by the value given by Einstein well-known formula E = mc2. In the rest of this book, when we are saying about information, which interacts with matter, we are meaning, that the wave is interacting with matter. Information is just expression of this wave, which is countable and visible, especially in Fourier space of this wave. Such a waves we will be calling Information waves. Returning to main point of this book. Action is the energy change over time. Information is described simply by a number. The minimum value of the action h (Planck's constant h = 6.62e-34 [Js]) is one bit of information. Information is not static, but dynamic. Formed by doing something, in short, action. The matter, however, is discrete but static. Well-known Einstein theory describes the conversion of mass to energy, means E = mc2. This can also be rewritten in a more general way, that the change of mass produces change of energy, ie. ΔE = Δmc2. If we now multiply both sides by a changing of time, in which this action took place, we get ΔEΔt = ΔmΔtc2. As already mentioned, the energy change over time, gives the action, which is generates amount of information of the value: 퐼 ∙ ℎ = 푐2 ∙ Δ푚 ∙ Δ푡 , (1) where I is the number of bits. This is the basic formula for the conversion of matter to waves which carry information. Informationism is a complete foundation of the world of physics. There are only discrete values, countable, limited and finite. Energy, as because is described by continuous values, does not exist in reality. It helps in the description of some phenomena. The idea of energy explains the some physics laws, but in reality the production of information waves causes phenomena made by energy (such as the atomic bomb).